Simplify the following expression: $ y = \dfrac{10}{-2q - 8} - \dfrac{3}{7} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{10}{-2q - 8} \times \dfrac{7}{7} = \dfrac{70}{-14q - 56} $ Multiply the second expression by $\dfrac{-2q - 8}{-2q - 8}$ $ \dfrac{3}{7} \times \dfrac{-2q - 8}{-2q - 8} = \dfrac{-6q - 24}{-14q - 56} $ Therefore $ y = \dfrac{70}{-14q - 56} - \dfrac{-6q - 24}{-14q - 56} $ Now the expressions have the same denominator we can simply subtract the numerators: $y = \dfrac{70 - (-6q - 24) }{-14q - 56} $ Distribute the negative sign: $y = \dfrac{70 + 6q + 24}{-14q - 56}$ $y = \dfrac{6q + 94}{-14q - 56}$ Simplify the expression by dividing the numerator and denominator by -2: $y = \dfrac{-3q - 47}{7q + 28}$